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FRBSF ECONOMIC LETTER
2013-27
September 23, 2013
Bubbles Tomorrow, Yesterday, but Never Today?
BY JOHN
C. WILLIAMS
Standard asset price models have generally failed to detect bubbles, with enormous costs to
the economy. Economists are now creating promising new models that account for bubbles by
relaxing the assumption of rational expectations and allowing people’s decisions to be driven by
their perceptions of what the future may hold. The following is adapted from a presentation by
the president and CEO of the Federal Reserve Bank of San Francisco to the National Association
for Business Economics in San Francisco, California, on September 9, 2013.
It’s a pleasure to be here at NABE’s 55th annual meeting. Your organization has done as much as any to
support the profession and promote discussion of the most important economic questions of our time, so
it’s a privilege to join you.
In my talk this morning, I will focus on an issue that has fascinated and perplexed economists for
centuries—asset price bubbles. Obviously, the events of the past two decades demonstrate that this topic
is not merely of academic interest. Asset price booms and busts distort the course of the economy and can
leave enormous economic wreckage in their trail. In considering this topic, I’ll start by reviewing the
basics of asset price theory. I’ll then highlight some striking inconsistencies between theory and evidence
in standard models of asset prices. I’ll then explore some recently developed theories that may help
explain why bubbles sometimes form and why they crash. And I’ll close with some speculation about the
implications for monetary and macroprudential policy.
We economists like to explain things using highly stylized models. We build make-believe worlds,
populate them with creatures that act according to strictly prescribed rules, and analyze what happens.
Or, as my wife said after I described one of my research papers to her: “You really never did stop playing
Dungeons and Dragons, did you?” The thing is, most of the time, this approach works remarkably well.
Often, the simplest model—with patently unrealistic assumptions—yields the keenest insights into how a
market or an economy works. Without doubt, Occam’s razor has proven to be a most valuable item in the
economics toolkit.
Unfortunately, asset prices have proven less amenable to this kind of treatment. A cursory reading of the
academic literature on asset prices reveals a litany of puzzles, conundrums, paradoxes, and anomalies.
Much of the research on asset prices continues to rely on highly stylized models with identical agents,
rational expectations, and optimizing behavior. According to the prevailing view, asset price surges that
many would perceive to be bubbles are not really so. Instead, they are seen to reflect the influences of
fundamental forces, such as a decline in risk appetite. This reminds me of the White Queen in Lewis
Carroll’s Through the Looking-Glass (1871), who says jam will be given every other day, but never today.
Adherents of this view may admit that bubbles have occurred in the past—like the dot-com boom and
bust. And they may even be willing to accept that bubbles are something to worry about in the future—
say, in financial supervision. But, in practice, they are never willing to find a bubble in the present.
FRBSF Economic Letter 2013-27
September 23, 2013
There’s always a reason why what looks like a bubble, walks like a bubble, and quacks like a bubble is not
actually a bubble. But, as I’ll discuss in a moment, this is changing. Recent research not only recognizes
that asset price bubbles really do form, but also holds great promise in unlocking their secrets and
identifying them.
Let’s now consider standard asset price theory, according to which the price of an asset equals the
discounted expected return of holding the asset for one period. For example, take a share in a
corporation. The return consists of two parts: the dividend payment the owner receives and the capital
gain or loss from selling the share. The same formula applies to owning a house or a bond, or any asset for
that matter. For the house, the dividend payment is the service flow the owner derives from living in it or
renting it out. For the bond, it is the coupon payment. According to this theory, three variables can affect
asset prices: the discount factor, the dividend payment, and the expected future price appreciation.
It helps to simplify things a bit further. Under certain assumptions, including the absence of bubble-like
behavior, Myron Gordon developed over 50 years ago an illuminating way of presenting this asset price
formula. He noted that the ratio of the asset price to the dividend payment is inversely related to the
difference between the expected future rate of return and the growth rate of inflation-adjusted dividends
(Gordon 1959). That is, all else equal, the price-to-dividend ratio should be high when expected future
dividend growth is high or when the expected future return to the asset is low. This is a classic case of an
elegant and parsimonious theory. So, how does it stand up to the data?
The first hurdle the model faces is the long history of boom and bust cycles in a variety of different asset
prices. These were thoroughly documented by Robert Shiller (2005) in his book Irrational Exuberance.
I’m an economist, so I need to show some numbers here. Figure 1 shows two well-known recent U.S. asset
price booms and busts. The thick blue line shows the price-to-dividend ratio of the S&P 500 stock index
from 1990 to the present. The thin red line shows the time series of the house price-to-rent ratio from the
CoreLogic home price index, in which
Figure 1
the rent data are the Bureau of
Asset price booms and crashes
Economic Analysis data on owners’
Ratio
equivalent rent. In the stock market
3.0
S&P 500
boom of the late 1990s, the price-toprice-to-dividend ratio
2.5
dividend ratio rose over 100% in the
five years up to the end of the boom in
2.0
2000. The recent housing boom was
relatively tame by this standard. The
1.5
house price-to-rent ratio climbed
around 50% during the five years
CoreLogic
1.0
before the market peak in 2006. To
house price-to-rent ratio
put these numbers in perspective,
0.5
according to flow of funds data, in the
five years before they peaked, U.S.
0.0
90 92 94 96 98 00 02 04 06 08 10 12
stock market wealth soared $12
Note: Normalized to 1 in January 1995.
trillion and housing wealth increased
Sources: CoreLogic, BEA, and S&P 500 data from Shiller (2005, updated).
some $10 trillion.
What does the Gordon model have to say about these and other large surges in asset prices? Two
explanations are possible based on changes in economic fundamentals. One is an upward shift in the
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FRBSF Economic Letter 2013-27
September 23, 2013
expected growth rate of future dividends. The second is a reduction in investors’ expected returns on the
asset. Importantly, in standard asset pricing theory, expectations of future dividend growth and future
returns on assets are assumed to be rational. That is, expectations are assumed to be consistent with the
structure of the model.
I’ll start with the first explanation, that a rise in the price-to-dividend ratio is caused by higher expected
dividend growth. The evidence on this is clear and negative. With respect to U.S. stocks, over history, the
price-to-dividend ratio is uncorrelated with future real dividend growth (Cochrane 2008). A similar
pattern is seen with regard to the U.S. housing market. The price-to-rent ratio is uncorrelated with future
real rent growth (Campbell et al. 2009 and Gelain and Lansing 2013). The international evidence is
somewhat more mixed. But a recent cross-country study found that, in most countries, the correlation
between the house price-to-rent ratio and future real rent growth is either statistically insignificant or has
the opposite sign of that predicted by the theory (Engsted and Pedersen 2012). Indeed, in the most recent
U.S. housing boom, the high house price-to-rent ratio observed during the boom did not foreshadow
subsequent high real rent growth. In fact, the growth rate of real rents actually declined in the period
following the peak price-to-rent ratio. It’s simply not the case that asset price movements can be
explained by shifts in rational expectations of future dividend growth.
So that leaves the possibility that a lower expected return might be driving the increase in asset prices
during a boom. The lower expected return could reflect a combination of lower alternative investment
returns, say as measured by the general level of real interest rates, and/or a lower risk premium on the
asset in question. As in the case of dividend growth, the evidence on expected future real interest rates
driving asset prices is negative. Equity dividend-to-price ratios are generally not correlated with future
changes in real interest rates (Campbell and Shiller 1988).
Thus, expectations of future dividends or real interest rates fail to explain asset price movements. Given
that, standard approaches ascribe much of the variation in asset prices to movements in the discount
factor used to compute the present value of future dividends. This is the logic of Sherlock Holmes in
Arthur Conan Doyle’s The Sign of the Four (1890), who said that, “when you have eliminated the
impossible, whatever remains, however improbable, must be the truth.” Time variation in the discount
factor is the only remaining rational explanation. However, on their own, you can’t really judge whether
movements in the discount factor are reasonable. After all, they are simply defined as the residual
component of an identity implied by the theory. In this regard, the discount factor is akin to total factor
productivity, which Moses Abramovitz (1956) famously described as “a measure of our ignorance.”
Moreover, the explanation that the discount factor is the main driver of movements in the price-todividend ratio has potentially falsifiable implications. In particular, it says that when the price-todividend ratio is high, rational investors should expect a relatively low rate of return on the asset. When
valuations are low, rational expected returns should be high (Greenwood and Shleifer 2013). For example,
if rational investors discount future dividends by less, perhaps owing to a reduction in risk aversion, then
the price-to-dividend ratio rises and we see a boom in the asset price. And the expected future rate of
return on the now higher-priced asset will be correspondingly lower.
So, are the data consistent with this prediction of the theory? One test is to compare real-world measures
of investors’ expected returns with the expected returns implied by the theory. Fortunately, there are a
number of surveys of investor expectations of future returns on stocks and houses that can be brought to
bear on this question.
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FRBSF Economic Letter 2013-27
September 23, 2013
Let me jump to the bottom line. The evidence from surveys of investors’ expected returns is directly at
odds with the implications of standard asset price theory. For one, stock market investors tend to expect
high future returns when the price-to-dividend ratio is high, contrary to the theoretical prediction of a
negative relationship between rational expected returns and the level of asset prices relative to dividends
(Greenwood and Shleifer 2013). A picture tells the story. Figure 2 shows Gallup survey results on the
relationship between the S&P 500
Figure 2
price-to-dividend ratio and investor
Stock prices and investor optimism
optimism regarding stock market
% optimistic - % pessimistic
returns over the next year. Gallup asks
80
whether people are optimistic,
60
pessimistic, or neutral about future
Fitted line
market returns. The figure reports the
40
difference between the number saying
20
they are optimistic or very optimistic
and those saying they are pessimistic
0
or very pessimistic. As the figure
-20
shows, periods of high stock
valuations, such as the late 1990s and
-40
mid-2000s, are when investors were
-60
more optimistic regarding future stock
0.5
1
1.5
2
2.5
3
S&P 500 price-to-dividend ratio
gains. And during periods of relatively
Sources: Greenwood and Shleifer (2013), Wells Fargo/Gallup, and S&P
low valuations, such as the early
500 data from Shiller (2005, updated). Thanks to the authors for
supplying data used in this figure. Data are from 1996 to 2013.
2000s and the period of the global
financial crisis, investors had
relatively low expectations of stock
Figure 3
market returns. The positive
House prices and expected price appreciation
relationship between current stock
Expected 1-yr house price change (%)
prices and expected future returns is
14
consistent across a variety of surveys
12
and alternative model specifications.
10
8
Fitted line
This same relationship is evident in
6
data on house prices. Figure 3 plots
4
the level of house prices and expected
2
future house price appreciation in the
United States over the past decade.
0
Each data point represents one of four
-2
major cities in a given year (Case,
-4
Shiller, and Thompson 2012). The
100
150
200
250
300
House price index
pattern is clear. Optimism about
Sources: S&P/Case-Shiller, FHFA, and Case, Shiller, and Thompson
future house price appreciation tends
(2012). Cities included are San Francisco/Alameda County, Boston, Los
to increase when house prices are
Angeles/Orange County, and Milwaukee. Data are from 2003 to 2012.
high. Just as with stocks, the survey
evidence directly contradicts the fundamental story that high house prices can be explained by a decline
in the rational expected return from homeownership.
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FRBSF Economic Letter 2013-27
September 23, 2013
Let me sum up my points so far. According to standard asset price theory, an increase in asset prices must
reflect either an increase in expected future dividend growth or a reduction in the expected return on the
assets. We see large run-ups in equity and home prices. But they are not associated with higher future
dividend growth rates or lower expected returns based on surveys. So far, this evidence is mainly
destructive. But, in fact, a first step to understanding asset price bubbles can be found in the survey data I
just discussed. The key is to relax the assumption of rational expectations and allow people’s decisions to
be driven by their perceptions of what the future may hold.
A striking regularity seen in the survey
data is that expectations of future
gains are highly positively correlated
with past observed returns. That is,
despite the admonition that past
performance is no guarantee of future
results, people appear to assume
exactly that in predicting future stock
returns. Figure 4 shows the
relationship between the Gallup
survey of investor optimism about
future stock market gains and the
trailing 12-month change in the S&P
500 stock price index. The correlation
is strongly positive. Indeed, the worst
reading for the investor optimism
index for the period shown in the
figure occurred in early 2009, just as
the stock market plunged to its
recession low. And the highest reading
of investor optimism occurred in early
2000, just before the tech stock crash.
The evidence is compelling. People
tend to extrapolate future stock price
movements from recent stock price
performance. This finding is
confirmed by econometric analysis
that uses different measures of
investor expectations and controls for
various other factors (Greenwood and
Shleifer 2013).
Figure 4
Extrapolative expectations in the stock market
% optimistic - % pessimistic
80
Fitted line
60
40
20
0
-20
-40
-60
-60
-40
-20
0
20
40
Trailing 12-month change in S&P 500 (%)
60
Sources: Greenwood and Shleifer (2013), Wells Fargo/Gallup, and S&P
500 data from Shiller (2005, updated). Thanks to the authors for
supplying data used in this figure. Data are from 1996 to 2013.
Figure 5
Extrapolative expectations in the housing market
Expected 1-yr house price change (%)
14
12
Fitted line
10
8
6
4
2
0
The same dynamic of extrapolative
expectations also plays out in housing
markets in the United States and
abroad. Figure 5 shows the
relationship between expected house
price appreciation over the next year
from surveys and the percentage
5
-2
-4
-30
-20
-10
0
10
20
30
Trailing 12-month change in house price indexes (%)
Sources: S&P/Case-Shiller, FHFA, and Case, Shiller, and Thompson
(2012). Cities included are San Francisco/Alameda County, Boston, Los
Angeles/Orange County, and Milwaukee. Data are from 2003 to 2012.
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FRBSF Economic Letter 2013-27
September 23, 2013
change in house prices observed over the prior year for four major U.S. cities over the past decade. As in
the case of stock prices, the correlation is strongly positive. Figure 6 shows similar patterns for Norway
and Sweden, two other countries that have experienced massive house price booms (Jurgilas and Lansing
2013). Just as in the United States,
Figure 6
when house prices go up, people
Scandinavia: House price expectations
expect them to continue to rise. And
A.
Norway
when they fall, people turn much more
% expecting increase - % expecting decrease
pessimistic about future house price
80
appreciation.
Many researchers are probing why
people have the procyclical pattern of
optimism seen in these surveys. One
key element in the theories coming
out of this research is that people do
not possess the full set of information
assumed in the standard asset price
model with rational expectations.
Instead, they must make do with the
limited information at hand when
judging likely future discounted
dividend payments and the future
price of the asset. Indeed, a growing
body of evidence in behavioral
economics and finance shows that
people’s expectations of future asset
returns depend on their past
experiences (Vissing-Jorgensen 2003
and Malmendier and Nagel 2011).
This process of forecasting with
limited information has been shown to
cause forecast errors that can drive a
wedge between asset prices and the
values implied by economic
fundamentals (Cutler, Poterba, and
Summers 1991 and Barsky and
DeLong 1993).
Fitted line
60
40
20
0
-20
-40
-10
-5
0
5
10
15
Trailing 12-month change in house price (%)
20
B. Sweden
% expecting increase - % expecting decrease
80
60
Fitted line
40
20
0
-20
-40
-60
-80
-5
0
5
10
Trailing 4-quarter change in house price (percent)
15
Source: Jurgilas and Lansing (2013). Data for Norway are from 2007 to
2012; data for Sweden are from 2003 to 2012.
The recognition that people behave this way can move us a long way closer to understanding how asset
price bubbles can emerge and how they can crash. To see this, let me return to the standard asset price
formula. Recall that the price of an asset equals the value of its dividend plus the discounted value of the
price at which you expect to be able to sell the asset. If one then assumes that investors’ expected price
appreciation of the asset depends positively on its recent past price change, this introduces a positive
feedback loop into asset price dynamics that is absent from the standard model assuming rational
expectations. Indeed, a simple model of extrapolative expectations of future asset price movements does a
very good job of explaining the big swings in the U.S. stock price-to-dividend ratio over time (Adam,
Beutel, and Marcet 2013).
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FRBSF Economic Letter 2013-27
September 23, 2013
This principle has proven a good model of investor expectations. But a challenge to models based on
extrapolative expectations is that they may create too much positive feedback in asset prices, producing
excess volatility at odds with the data. Despite the failures of standard asset price theory, the price-todividend ratio is a good predictor of future excess returns on the stock market relative to the risk-free rate
(Cochrane 2008). That is, a high price-to-dividend ratio today predicts relatively low average future stock
returns. Therefore, for a model to succeed, it needs to allow for procyclical investor optimism, while
incorporating a self-stabilizing mechanism that eventually stops and reverses this process, bringing prices
back toward fundamental values. This is a delicate balance. One promising approach is to posit two types
of traders, one with extrapolative expectations and the other that trades based on fundamentals (Cutler,
Poterba, and Summers 1990 and Greenwood and Shleifer 2013). In a nutshell, the traders with
extrapolative expectations drive the procyclical optimism, while the fundamental traders exert a
stabilizing influence that keeps things from going completely off the rails (see Adam et al. 2013 for an
alternative approach).
Researchers have yet to coalesce around one preferred model. However, a common theme in this
literature is that the presence of a small amount of sand in the ability of people to process information can
lead to large and sustained swings in asset prices, with significant repercussions for the economy. An
important implication of these models is that nonfundamental asset price movements do not represent
exogenous “shocks” to the economy. Rather, they are part of the endogenous behavior of the economic
system. In particular, these asset price movements tend to amplify and propagate other shocks that occur
within the system.
This recognition of the source of asset price movements means that work on monetary and
macroprudential policies needs to refocus on how these policies may damp or amplify asset price cycles,
rather than how they should respond to asset prices per se. For monetary policy, one implication of
theories with endogenous asset price bubbles is that the time horizon over which policy affects the
economy may be longer than typically thought. In particular, the policy response to cyclical movements in
economic activity and inflation may have effects on investor beliefs and the behavior of asset prices that
reach well into the future.
The lesson from history is clear: asset price bubbles and crashes are here to stay. They appear to be a
consequence of human nature (Kindleberger 1978). And the events of the past decade demonstrate the
enormous human costs of asset price bubbles and crashes.
To understand the past and avoid a recurrence of the devastating events we lived through so recently, we
need to acknowledge that investors and financial markets do not behave the way rational asset price
theory implies. We need to incorporate these channels into the models we use for forecasting, risk
analysis, and policy evaluation. This opens up a world where actions, including regulatory and monetary
policy measures, may have unintended consequences—such as excessive optimism, risk taking, and the
formation of bubbles—that are assumed away in standard rational models.
Of course, this is a difficult task, and successful models are likely to be far more complicated than the
simple and elegant rational models we have relied on in the past. But, it’s essential if we want to design
policies that foster robust economic performance in the future.
John C. Williams is president and chief executive officer of the Federal Reserve Bank of San Francisco.
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FRBSF Economic Letter 2013-27
September 23, 2013
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